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<body bgcolor="aqua"><center><h2>Averages</h2></center>
<pre>
<font size="2">
<strong>Formula:</strong>
1.Average=Sum of quantities/Number of quantities.
2.Suppose a man covers a certain distance at x kmph
and an equal distance at y kmph ,then the average speed
during the whole journey is (2xy/x+y) kmph.
<b>Examples: </b>
1.Find the average of all these numbers.142,147,153,165,157.
Solution:
142 147 153 165 157
Here consider the least number i.e, 142
comparing with others,
142 147 153 165 157
+5 +11 +23 +15
Now add 5+11+23+15 = 52/5 = 10.8
Now add 10.8 to 142 we get 152.8
(Average of all these numbers).
Answer is 152.8
2.Find the average of all these numbers.4,10,16,22,28
Solution:
4,10,16,22,28
As the difference of number is 6
Then the average of these numbers is central one i.e, 16.
Answer is 16.
3.Find the average of all these numbers.4,10,16,22,28,34.
Solution:
Here also difference is 6.
Then middle numbers 16,22 take average of these
two numbers 16+22/2=19
Therefore the average of these numbers is 19.
Answer is 19.
4.The average marks of a marks of a student in 4 Examination
is 40.If he got 80 marks in 5th Exam then what is
his new average.
Solution:
4*40+80=240
Then average means 240/5=48.
Answer is 48.
5.In a group the average income of 6 men is 500 and that
of 5 women is 280, then what is average income of the group.
Solution:
6*500+5*280=4400
then average is 4400/11=400.
Another Method: here consider for 6 men
6 men – each 500.
so 5th women is 280.
then 500-280=220.
then 220*6/11=120.
therefore 120+280=400.
Answer is 400.
6.The average weight of a class of 30 students is 40 kgs if the
teacher weight is included then average increases by 2 kgs then
find the weight of the teacher?
Solution:
30 students average weight is 40 kgs.
So,when teacher weight is added it increases by 2 kgs
so total 31 persons ,therefore 31*2=62.
Now add the average weight of all student to it
we get teachers weight i.e, 62+40=102 kgs.
Answer is 102 kgs.
7.The average age of Mr and Mrs Sharma 4 years ago is 28 years .
If the present average age of Mr and Mrs Sharma and their son
is 22 years. What is the age of their son.
Solution:
4 years ago their average age is 28 years.
So their present average age is 32 years.
32 years for Mr and Mrs Sharma then 32*2=64 years.
Then present age including their son is 22 years.
So 22*3 =66 years.
Therefore son age will be 66-64 = 2 years.
Answer is 2 years.
8.The average price of 10 books is increased by 17 Rupees when
one of them whose value is Rs.400 is replaced by a new book.
What is the price of new book?
Solution:
10 books Average increases by 17 Rupees
so 10*17= 170.
so the new book cost is more and by adding its cost average
increase,therefore the cost of new book is 400+170=570Rs.
Answer is 570 Rs.
9.The average marks of girls in a class is 62.5. The average marks
of 4 girls among them is 60.The average marks of remaining girls
is 63,then what is the number of girls in the class?
Solution:
Total number of girls be x+4.
Average marks of 4 girls is 60.
therefore 62.5-60=2.5
then 4*2.5 =10.
the average of remaining girls is 63
here 0.5 difference therefore 0.5*x=10(since we got from 4 girls)
(this is taken becoz both should be equal)
x=10/0.5
x=20.
This clear says that remaining are 20 girls
therefore total is x+4=20+4=24 girls
Answer is 24 girls.
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10.Find the average of first 50 natural numbers.
Solution:
Sum of the Natural Numbers is n(n+1)/2
therefore for 50 Natural numbers 50*51/2=775.
the average is 775/50=15.5
Answer is 15.5 .
11.The average of the first nine prime number is?
Solution:
Prime numbers are 2,3,5,7,11,13,17,19,23
therefore 2+3+5+7+11+13+17+19+23=100
then the average 100/9= 11 1/9.
Answer is 11 1/9.
12.The average of 2,7,6 and x is 5 and the average of and the
average of 18,1,6,x and y is 10 .what is the value of y?
Solution:
2+7+6+x/4=5
=>15+x=20
=>x=5.
18+1+6+x+y/5=10
=>25+5+y=50
=>y=20.
13.The average of a non-zero number and its square is 5 times the
number.The number is
Solution:
The number be x
then x+x2/2=5x
=>x2-9x=0
=>x(x-9)=0
therefore x=0 or x=9.
The number is 9.
14.Nine persons went to a hotel for taking their meals . Eight of
them spent Rs.12 each on their meals and the ninth spent Rs.8 then
the average expenditure of all the nine. What was the total money
spent by them?
Solution:
The average expenditure be x.
then 8*12+(x+8)=9x
=>96+x+8=9x.
=>8x=104
=>x=13
Total money spent =9x=>9*13=117
Answer is Rs.117
15.The average weight of A.B.C is 45 Kgs.If the average weight of
A and B be 40 Kgs and that of Band C be 43 Kgs. Find the weight of B?
Solution:
The weight of A,B,Care 45*3=135 Kgs.
The weight of A,B are 40*2=80 Kgs.
The weight of B,C are 43*2=86 Kgs.
To get the Weight of B.
(A+B)+(B+C)-(A+B+C)=80+86-135
B=31 kgs.
Answer is 31 Kgs.
16.The sum of three consecutive odd number is 48 more than the average
of these number .What is the first of these numbers?
Solution:
let the three consecutive odd numbers are x, x+2, x+4.
By adding them we get x+x+2+x+4=3x+6.
Then 3x+6-(3x+6)/3=38(given)
=>2(3x+6)=38*3.
=>6x+12=114
=>6x=102
=>x=17.
Answer is 17.
17.A family consists of grandparents,parents and three grandchildren.
The average age of the grandparents is 67 years,that of parents is 35
years and that of the grand children is 6 years . What is the average
age of the family?
Solution:
grandparents age is 67*2=134
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